Rewrite as a simplified fraction. ${1.9\overline{51} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 1951.5151...\\ 10x &= 19.5151...\end{align*}}$ Subtracting the two equations, we have: ${990x = 1932}$ ${x = \dfrac{1932}{990}} $ ${x = \dfrac{322}{165}} \text{or} {1 \dfrac{157}{165}}$